Question

When working with rational exponents, does it matter if we take the root first or if we take the power? Also, can this be solved?....
Example: 64/5 = ^5√6^4

Answer 1

not sure what you mean by what you take first?
yes
\[6^{4/5} = \sqrt[5]{6^{4}}\]
the root will always be the denominator of the rational exponent

Answer 2

I'm not sure either... instructor asked me a couple odd questions that I don't quite understand!

Answer 3

Just do the power always first . You can't go wrong

Answer 4

there is a rule behind it but i don't remember

Answer 5

you can take either but for example
8^(5/3) it is easier to take cube root of 8 = 2 rather than find cube root of 8^5

Answer 6

And the example is already fully solved, isn't it??

Answer 7

yes